ACKNOWLEDGEMENTS ................................................ V
PREFACE ....................................................... VII
TABLE OF CONTENTS .............................................. XI
LIST OF FIGURES ................................................ XV
LIST OF TABLES ............................................... XVII
LIST OF ABBREVIATIONS AND SYMBOLS ............................. XIX
ABSTRACT .................................................... XXIII
1 INTRODUCTION ................................................. 1
1.1 Background .............................................. 2
1.2 scope and methodology of the research ................... 5
1.3 Problem statement and primary research objectives ....... 7
1.4 Organization of the thesis .............................. 7
2 BACKGROUND ................................................... 9
2.1 Terminologies and guiding principles of probabilistic
design, risk and safety analysis ........................ 9
2.2 Risk analysis methods .................................. 14
2.3 Risk analysis process .................................. 16
2.4 Related Works .......................................... 18
2.4.1 On basic theories of probabilistic design,
risk and safety analysis ........................ 19
2.4.2 On applications to hydraulic engineering ........ 19
3 MONTE CARLO SIMULATION AND APPROXIMATE MOMENT ANALYSIS
METHODS ..................................................... 21
3.1 The Monte Carlo Simulation Method (MCSM) ............... 21
3.2 The Moment Analysis Approximation Methods (MAM) ........ 24
3.2.1 MAM for linear FRV .............................. 25
3.2.2 MAM for FRV involving products .................. 26
3.2.3 MAM for FRV involving positive integer powers ... 28
3.2.4 The FOSM and SOSM approximate moment analysis
methods ......................................... 28
3.3 Summary of other classical approximate methods ......... 35
3.3.1 The method of reliability index (fS) ............ 36
3.3.2 Point estimate (PE) methods ..................... 39
3.3.3 The Latin Hypercube sampling method ............. 43
4 AN ANALYTICAL METHOD FOR TRANSFORMING PDFS .................. 45
4.1 Definitions and Notations .............................. 45
4.2 Problem statement ...................................... 46
4.3 The analytical method .................................. 47
4.3.1 The uni-variate FRV ............................. 47
4.3.2 The case of multivariate FRV .................... 50
4.4 Application procedures and requirements ................ 53
4.5 Chapter conclusions .................................... 55
5 DAM ENGINEERING AND THE CASE STUDY DAM: PROBABILISTIC
PERSPECTIVES ................................................ 57
5.1 Review on major causes of dam failure and their
statistics ............................................. 57
5.1.1 Types of dams ................................... 57
5.1.2 Major causes of dam failure and their
statistics ...................................... 57
5.2 Embankment dams failure mechanisms and design
practices .............................................. 58
5.2.1 Classical design practices and standards for
slope stability ................................. 61
5.2.2 Classical design practices and standards for
flood and wave protection ....................... 70
5.3 The case study dam (Tendaho Dam, Ethiopia) and awash
River basin ............................................ 75
5.3.1 General ......................................... 75
5.3.2 The Awash River ................................. 76
5.3.3 Salient features of Tendaho Dam project ......... 81
5.3.4 Tendaho Dam basic design considerations and
deterministic compliance of design
requirements .................................... 82
5.4 Data used .............................................. 83
5.4.1 Resistance related data ......................... 85
5.4.2 Load related data ............................... 87
5.4.3 Porewater pressure data, geometry, scheme of
meshing and FEM stability and seepage analysis
of Tendaho Dam .................................. 93
5.5 Evaluation of uncertainty of strength and load
parameters-stability ................................... 95
5.5.1 Uncertainty in fill materials selected
engineering properties .......................... 96
5.6 Evaluation of uncertainty of strength and load
parameters-overtopping ................................. 98
6 APPLICATIONS OF THE PROPOSED PROBABILISTIC AND ANALYTICAL
METHODS - EMBANKMENT DAM STABILITY AND SEEPAGE PROBLEMS .... 101
6.1 Introduction .......................................... 101
6.2 Computational framework and case study synthesis ...... 102
6.3 Analytical solution (ASDD method) ..................... 106
6.3.1 Load-shear stress (G) .......................... 107
6.3.2 Strength- shear strength (τ) ................... 111
6.3.3 Stability performance ƒFS,S, (FSS) and Pƒ,s ...... 115
6.4 Classical probabilistic methods solutions (MCSM,
FOSM, SOSM methods) ................................... 115
6.4.1 FOSM and SOSM solutions ........................ 115
6.4.2 MCSM solution .................................. 116
6.5 Seepage flux .......................................... 116
6.6 Comparison of results ................................. 117
6.7 Chapter conclusions ................................... 119
7 APPLICATIONS OF THE PROPOSED PROBABILISTIC AND ANALYTICAL
METHODS - DAM OVERTOPPING PROBLEM .......................... 121
7.1 Introduction .......................................... 121
7.2 The framework ......................................... 122
7.3 Random variables, analysis and representation
methods ............................................... 124
7.3.1 Flood surcharge (hƒ) ........................... 124
7.3.2 Initial water level (h0) ....................... 132
7.3.3 Wave height-wave run up and wind setup
(hr, hs) ....................................... 133
7.4 Stochastic models and solution procedure .............. 139
7.5 Results and discussions ............................... 149
7.6 Chapter conclusions ................................... 152
8 CONCLUSIONS AND RECOMMENDATIONS ............................ 153
8.1 On the deterministic and stochastic/analytical
methods ............................................... 153
8.2 on seepage and sliding probability analyses ........... 155
8.3 on dam overtopping probability analysis ............... 156
8.4 recommendations and outlooks .......................... 157
9 APPENDICES ................................................. 161
9.1 APPENDIX TO CHAPTER TWO AND THREE ..................... 161
9.1.1 Statistical and mathematical background ........ 161
9.1.2 Review on common probability density
functions in engineering practice .............. 185
9.1.3 Fitting distributions to data .................. 196
9.2 Appendix то chapter four .............................. 198
9.3 Appendix то chapter five .............................. 199
9.3.1 Tendaho Dam main features ...................... 199
9.3.2 Type, form and sources of data collected on
Tendaho Dam during the fieldwork ............... 201
9.3.3 Selected Tendaho dam core and shell material
properties ..................................... 204
9.3.4 Historical mean monthly, mean annual and
annual maximum flow of Awash River at
Tendaho ........................................ 206
9.3.5 Monthly flow and sediment data of Awash River
at Dubti (based on measurements made by
Sogreah between 1962-1964, source (Sogreah,
1965)) ......................................... 208
9.3.6 Monthly flow and sediment data of Awash River
at Dubti (based on measurements made by MoWR
department of hydrology over the period 1985-
1987, source MoWR) ............................. 208
9.3.7 Monthly sediment load of Awash River
generated using flow-sediment load
relationship derived based Sogreah data ........ 209
9.3.8 Mean annual sediment load of the Awash River
at the Tendaho dam site generated based on
two different rating equations ................. 211
9.3.9 Tendaho Dam elevation storage-area
relationship at year 0, 25 and 50 .............. 213
9.3.10 Generated long term (50 years) flows for
Tendaho Dam (after WWDSE, 2005) ................ 214
9.3.11 Historic wind speed records used in Tendaho
Dam wave height analysis ....................... 214
9.4 Appendix то chapter six ............................... 215
9.4.1 SOSM approximation for moments and
uncertainty of shear strength (τ) .............. 215
9.4.2 FOSM approximation for moments and
uncertainty of shear strength (τ) .............. 218
9.4.3 SOSM and FOSM approximation of moments and
uncertainty of shear stress (G) ................ 219
9.4.4 SOSM and FOSM approximation of reliability
(ZS), sliding factor of safety (FS,S) and
sliding failure probability (Pƒ,S) .............. 221
10 REFERENCES ................................................. 229
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